By Timothy Banas • Updated March 24, 2022

FactoryTh/iStock/GettyImages

Engineers create solenoids—electromagnets—by winding conductive wire into a spiral around a cylindrical core. When an electric current flows through the coil, a magnetic field is generated that can exert a measurable pull on nearby ferromagnetic materials. The resulting interaction between magnetic and electric forces on a charged particle is known as the Lorentz force.

Step 1 – Write the Formula

The force produced by a solenoid can be calculated with the following expression:

F = ((n·I)² × μ₀ × A) ÷ (2·g²)

Where:
– F = force (Newtons)
– I = current through the coil (Amperes)
– g = gap distance between the coil and the target metal (meters)
– A = cross‑sectional area of the coil (square meters)
– n = number of turns in the coil
– μ₀ = magnetic constant (4π × 10⁻⁷ H/m)

Step 2 – Gather Your Parameters

Before plugging numbers into the equation, determine the physical attributes of your electromagnet and the operating conditions. For instance:

• Number of turns (n) = 1,000
• Current (I) = 10 A
• Cross‑sectional area (A) = 0.5 m²
• Gap distance (g) = 1.5 m

Step 3 – Compute the Force

Substitute the values into the formula:

F = (((1,000 × 10)² × 4π × 10⁻⁷ × 0.5) ÷ (2 × 1.5²)) ≈ 14 N

This result indicates that, under the specified conditions, the electromagnet will exert a pull of approximately fourteen newtons on a ferromagnetic object placed 1.5 meters away.

By following these straightforward steps, you can accurately predict the performance of any solenoid‑based electromagnet you design or evaluate.